Gravity is the force of inherent natural attraction between two massive bodies. The magnitude of the gravitational force is directly related to the mass of the bodies and is inversely related to the square of the distance between centers of mass of the two attracted bodies.
Gravity is measured as acceleration, g, usually as a vertical vector component. The freefall acceleration, g, of an object near the surface of the earth is given to a first approximation by the gravitational attraction of an object with the mass of the entire earth, Me, located at the center of the earth, a distance, Re, from the surface of the earth. This nominal gravity value, g=G×Me/Re2, is about 9.8 m/s2. Thus, the freefall acceleration due to gravity near the earth's surface of an object having a small mass compared to the mass of the earth is about 9.8 m/s2. The common unit of measurement for gravity is the “Galileo” (Gal), which is a unit of acceleration defined as 1 cm/s2. One Gal generally approximates 1/1000 (10−3) of the force of gravity at the earth's surface.
An instrument which measures gravity is called a “gravimeter.” The most accurate gravimeters are absolute gravimeters. A typical interferometric absolute gravimeter uses a freely falling test mass and a laser or single-frequency light beam which impinges upon and reflects from the freely falling test mass. The path length of the light beam changes as it is reflected from the freely falling test mass. The reflected light beam is combined with a reference light beam to develop interference fringes. Interference fringes are instances where the amplitude or intensity of the reflected and reference light beams add together to create increased intensity, separated by instances where the two beams cancel or create diminished intensity.
Fringes occur on a periodic basis depending upon the relative change in the optical path lengths of two combined light beams. One fringe occurs whenever the optical path length difference changes by one wavelength. When the beam path reflects from a moving object, the beam path length changes by twice the amount of physical movement, because the physical movement changes both the impinging and reflection paths of the light beam. For reflections, a fringe typically occurs when the object moves by one-half of a wavelength. The fringes taken together as a set comprise a record of the distance that the object moves.
The occurrence and timing of the resulting interference fringes defines the characteristic of gravity, because the gravity establishes the freefall movement of the test mass. The use of optical fringe interferometry to measure gravity characteristics is well-known, as is described in U.S. Pat. No. 5,351,122.
A gradient of gravity is the rate at which gravity changes over a certain distance. A gravity gradient is therefore the change or first derivative of the gravity over distance. An instrument used to measure a gradient of gravity is called a “gradiometer.”
Although the gradient of gravity can be determined in any direction, the vertical gradient of gravity is useful in many practical applications. Vertical gravity gradients identify changes in density or mass of a particular material or geological structure. For example, gravity gradients are used to establish the location of underground geological structures, such as a pool of liquid petroleum encased within an earth formation, narrow seams or “tubes” of high density geological materials such as diamonds or cobalt, or voids in a geographical formation caused by a tunnel or cavern. These changes in the subterranean material density are most measurable within a relatively short near-field distance, typically within a few hundred meters.
Subsurface density anomalies, for example from valuable nearby high density ore bodies or voids caused by tunnels or areas of low density material, affect the local value of gravity, g, at a level of about 1 part per million ( 1/106), and in some cases 1 part per billion ( 1/109). The large background of the earth's gravity requires that any direct gravity measurement to detect such subsurface anomalies have a very large dynamic range of parts per billion, otherwise direct gravity measurements will not be possible or accurate. It is difficult to make gravimeters with such levels of extremely high precision, so it is desirable to find ways to cancel the large effect of the earth's gravity while preserving the ability to detect gradations in nearby density anomalies.
The vertical gravity gradient of the earth is typically measured in terms of a unit called the Eotvos unit, E, given by 10−9/s2. The vertical gravity gradient of the entire earth is typically about 3000E. Typical nearby mass anomalies can affect the vertical gravity gradient at a level of about 1E or more. Thus, the contrast of the vertical gravity gradient caused by nearby mass anomalies to the earth's vertical gravity gradient is about 300,000 (3×105) times larger than for the gravity value itself. This means that a vertical gravity gradiometer can have 3×105 times less precision than a gravimeter and still be used effectively to detect or locate nearby mass or density anomalies.
A gradiometer removes the background effect of gravity. Logically, a gradiometer differences the gravity measurements at two different nearby locations. A known vertical gravity gradiometer is made by placing two gravimeters above one other with a vertical separation of fixed distance, z, and then subtracting the two gravity measurements, g1 and g2. The vertical gravity gradient, γ, is then given by the ratio of this difference divided by the vertical separation, i.e. γ=(g2−g1)/z. This quantity is also mathematically referred to as the spatial derivative of gravity in the vertical direction.
Although implementing a gradiometer is conceptually straightforward, the practical reality of doing so involves many significant and practical problems. Using two gravimeters, one above the other, subtracting their absolute measurements and dividing by the distance between the two gravimeters, almost invariably leads to inaccurate measurements. Each gravimeter is subject to many naturally-occurring and man-made vibrations and other physical perturbations. These effects influence each gravimeter differently. These vibrations and perturbations cause minute changes in the path length of the light beams, causing anomalous interference fringes which are unrelated to the gravity characteristic under measurement and thereby reduce the accuracy of the measurement, or at minimum enhance the potential for errors.
Attempts have been made to employ common mode rejection to eliminate the anomalous vibration and perturbation errors in interferometric gravimeters and gradiometers. Since it is virtually impossible to control anomalous vibrations and perturbations, attempts to achieve common mode rejection involve subjecting the light beams to the same physical influences, thereby allowing the same anomalous influences to equally affect both light beams. Theoretically, when the two light beams are combined, the anomalous common error in both signals is theoretically canceled or rejected because of the cancellation of those effects resulting from the combination.
One effective use of common mode rejection in an interferometric gradiometer is described in U.S. patent application Ser. No. 13/558,138, filed Jul. 25, 2012 by the inventors herein and assigned to the assignee hereof, now U.S. Pat. No. 8,978,465. In this prior invention, two separate light beams which traverse separate beam paths impinge upon and reflect from two separate freely falling test masses. Any vibration and perturbation anomalies of the test masses are effectively canceled by common mode rejection. In this regard the prior invention is a substantial improvement over previously known gravimeters.
However, the stationary optical elements, which direct the two separate light beams, are subject to individually separate and different anomalous vibrations and perturbations which adversely influence the lengths of each of the two light beams separately and uniquely. Combining the beams to create the fringes does not achieve common mode cancellation of these separate and unique adverse influences, but instead may create anomalous fringes which lead to measurements of compromised accuracy.